First, we develop a general model (GM) with a futures market that requires physical delivery when the spot market takes place. Then, we consider a market where the futures market makes use of contracts for differences (CFD).
CFD is a financial instrument that makes it possible for the players in the market to hedge against the difference between the futures price and the spot market price in a future time period, and serves as a market coordination mechanism.
For comparison we also analyze the spot market without the presence of futures trading. To deal with both risk averse and risk neutral generators, we introduce a coherent risk measure (Conditional Value at Risk, CVaR) which has been extensively used in the literature after its introduction by [1]} for portfolio optimization problemsAlthough VaR is a well-known risk measure in economic problems, it is a non-coherent risk measure suffering from non-convexity, non-smoothness, subadditivity, etc., which makes it undesirable in optimization programs. To avoid this problem, there is an attractive alternative risk measure identified as CVaR also known as average value at risk or mean shortfall. CVaR is a risk assessment technique often used to reduce the probability a portfolio will incur large losses. This is performed by assessing the likelihood (at a specific confidence level \(\alpha \) ) that a specific loss will exceed the value at risk. That is, CVaR is derived by taking a weighted average between the VaR and losses exceeding the VaR.. We derive analytical relationships between contracts and study the implications of demand, production cost, and RES capacity uncertainties on electricity market outcomes. Finally, the performance of the proposed equilibrium model and its main properties are tested with extensive numerical simulations. Our results show that overall electricity prices, generation costs, profits, and quantities decrease for conventional generators, whereas quantities and profits increase for RES generators with respect to the level of RES penetration. Despite physical and financial contracts exhibit different impacts on the resulting equilibrium market outcomes, they both efficiently mitigate the impact of uncertainties and facilitate the integration of RES into the electricity system. Moreover, risk aversion increases profit and decreases generators' risk in the general model for both the Cournot and perfect competitions, which is a counter-intuitive result. That is because contracts increase market participants' willingness to participate in the market as it shields them from the risk associated with production cost, demand, and RES uncertainties.
